		Search-engine friendly clone of the ACL2 documentation.

Topdecl

Topdecl-fix

Fixing function for topdecl structures.

Signature
(topdecl-fix x) → new-x
Arguments: x — Guard (topdeclp x).
Returns: new-x — Type (topdeclp new-x).

Definitions and Theorems

Function: topdecl-fix$inline

(defun topdecl-fix$inline (x)
 (declare (xargs :guard (topdeclp x)))
 (let ((__function__ 'topdecl-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (topdecl-kind x)
     (:function (b* ((get (fundecl-fix (std::da-nth 0 (cdr x)))))
                  (cons :function (list get))))
     (:struct (b* ((get (structdecl-fix (std::da-nth 0 (cdr x)))))
                (cons :struct (list get))))
     (:mapping (b* ((get (mappingdecl-fix (std::da-nth 0 (cdr x)))))
                 (cons :mapping (list get)))))
   :exec x)))

Theorem: topdeclp-of-topdecl-fix

(defthm topdeclp-of-topdecl-fix
  (b* ((new-x (topdecl-fix$inline x)))
    (topdeclp new-x))
  :rule-classes :rewrite)

Theorem: topdecl-fix-when-topdeclp

(defthm topdecl-fix-when-topdeclp
  (implies (topdeclp x)
           (equal (topdecl-fix x) x)))

Function: topdecl-equiv$inline

(defun topdecl-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (topdeclp acl2::x)
                              (topdeclp acl2::y))))
  (equal (topdecl-fix acl2::x)
         (topdecl-fix acl2::y)))

Theorem: topdecl-equiv-is-an-equivalence

(defthm topdecl-equiv-is-an-equivalence
  (and (booleanp (topdecl-equiv x y))
       (topdecl-equiv x x)
       (implies (topdecl-equiv x y)
                (topdecl-equiv y x))
       (implies (and (topdecl-equiv x y)
                     (topdecl-equiv y z))
                (topdecl-equiv x z)))
  :rule-classes (:equivalence))

Theorem: topdecl-equiv-implies-equal-topdecl-fix-1

(defthm topdecl-equiv-implies-equal-topdecl-fix-1
  (implies (topdecl-equiv acl2::x x-equiv)
           (equal (topdecl-fix acl2::x)
                  (topdecl-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: topdecl-fix-under-topdecl-equiv

(defthm topdecl-fix-under-topdecl-equiv
  (topdecl-equiv (topdecl-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-topdecl-fix-1-forward-to-topdecl-equiv

(defthm equal-of-topdecl-fix-1-forward-to-topdecl-equiv
  (implies (equal (topdecl-fix acl2::x) acl2::y)
           (topdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-topdecl-fix-2-forward-to-topdecl-equiv

(defthm equal-of-topdecl-fix-2-forward-to-topdecl-equiv
  (implies (equal acl2::x (topdecl-fix acl2::y))
           (topdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: topdecl-equiv-of-topdecl-fix-1-forward

(defthm topdecl-equiv-of-topdecl-fix-1-forward
  (implies (topdecl-equiv (topdecl-fix acl2::x)
                          acl2::y)
           (topdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: topdecl-equiv-of-topdecl-fix-2-forward

(defthm topdecl-equiv-of-topdecl-fix-2-forward
  (implies (topdecl-equiv acl2::x (topdecl-fix acl2::y))
           (topdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: topdecl-kind$inline-of-topdecl-fix-x

(defthm topdecl-kind$inline-of-topdecl-fix-x
  (equal (topdecl-kind$inline (topdecl-fix x))
         (topdecl-kind$inline x)))

Theorem: topdecl-kind$inline-topdecl-equiv-congruence-on-x

(defthm topdecl-kind$inline-topdecl-equiv-congruence-on-x
  (implies (topdecl-equiv x x-equiv)
           (equal (topdecl-kind$inline x)
                  (topdecl-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-topdecl-fix

(defthm consp-of-topdecl-fix
  (consp (topdecl-fix x))
  :rule-classes :type-prescription)